The first case of two consecutive integers which are sphenic numbers is 230 = 2×5×23 and 231 = 3×7×11. The first case of three is 1309 = 7×11×17, 1310 = 2×5×131, and 1311 = 3×19×23. There is no case of more than three, because one of every four consecutive integers is divisible by 4 = 2×2 and therefore not squarefree.
the largest known sphenic number is (243,112,609 − 1) × (237,156,667 − 1) × (232,582,657 − 1), i.e., the product of the three largest known primes.